Burghelea-Friedlander-Kappeler's gluing formula and the adiabatic decomposition of the zeta-determinant of a Dirac Laplacian

2003/04/23 by Yoonweon Lee, Lee, Yoonweon
Chemistry · Mathematics · #58J50 #58J52 #Advanced NMR Techniques and Applications #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory in Mathematical Physics #math.DG #msc:58J50 #msc:58J52

paper · pdf · doi:10.48550/arxiv.math/0304347

22pages

openalex publication_date 2003/04/23 · arxiv created 2003/04/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we first establish the relation between the zeta-determinant of a Dirac Laplacian with the Dirichlet boundary condition and the APS boundary condition on a cylinder. Using this result and the gluing formula of the zeta-determinant given by Burghelea, Friedlander and Kappeler with some assumptions, we prove the adiabatic decomposition theorem of the zeta-determinant of a Dirac Laplacian. This result was originally proved by J. Park and K. Wojciechowski in [11] but our method is completely different from the one they presented.

Related

• Burghelea-Friedlander-Kappeler's gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion
• The gluing formula of the zeta-determinants of Dirac Laplacians for certain boundary conditions
• The ratio of two zeta-determinants of Dirac Laplacians associated with unitary involutions on a compact manifold with cylindrical end
• The BFK type gluing formula of zeta-determinants for the Robin Boundary condition
• Adiabatic decomposition of the zeta-determinant and Scattering theory